I’m flinching at a painful sense of déjà vu as we hear calls for military intervention in Iraq, as President Barack Obama himself — taunted by critics who contend he’s weak — is said to be considering drone strikes there.

Our 2003 invasion of Iraq should be a warning that military force sometimes transforms a genuine problem into something worse. The war claimed 4,500 American lives and, according to a mortality study published in a peer-reviewed American journal, 500,000 Iraqi lives. Linda Bilmes, a Harvard expert in public finance, tells me that her latest estimate is that the total cost to the United States of the Iraq War will be $4 trillion.

That’s a $35,000 tax on the average U.S. household. The total would be enough to ensure that all children could attend preschool in the United States, that most people with AIDS worldwide could receive treatment, and that every child worldwide could attend school — for the next 83 years. Instead, we financed a futile war that was like a Mobius strip, bringing us right back to an echo of where we started.

We might have learned some humility. Yes, the military toolbox is handy and often useful. But one of the most basic lessons of international relations is a frustrating one: There are more problems than solutions. Governments, like doctors, should weigh the principle, “First, do no harm.”

Yet Paul Bremer, the former U.S. envoy in Iraq, argues for air strikes and even a few boots on the ground. The Wall Street Journal’s editorial page, likewise, favors military intervention.

Perhaps more surprisingly, so does Sen. Dianne Feinstein, D-Calif., the chairwoman of the Senate Intelligence Committee. “I think most important is that we take direct action now against ISIS,” she said, according to the Washington newspaper The Hill, in reference to the Islamic State of Iraq and the Levant, the Sunni militant group that has swept into northern Iraq.

The least surprising hawk is Dick Cheney, who in a Wall Street Journal op-ed article with his daughter Liz preserves an almost perfect record of being wrong. From the vice president who himself obtained every possible deferment to avoid Vietnam, who asserted “with absolute certainty” in 2002 that Saddam was making nuclear weapons, and insisted in 2005 that the Iraqi insurgency was in its “last throes,” we now have a blast at President Barack Obama for failing to extinguish the continuing throes.

Iraq has formally requested U.S. military intervention, and my fear is that we will be inadvertently sucked into a civil war — an echo of what happened to the United States in Lebanon from 1982 to ’84 or Somalia from 1992 to ’94. Look, failing to intervene is a bad option in this case. But intervening is a worse one.

Let’s acknowledge that hawks are right, that Iraq presents a serious problem. But is U.S. military intervention really the best response at this time? Not at all.

Remember that the militants’ invasion was accomplished by a tiny force of perhaps 4,000 fighters, and that Iraq has an army 50 times as large. It’s possible for the Shiite-led Iraqi government of Prime Minister Nouri al-Maliki to defeat the militants, but the essential first step is for al-Maliki (or a replacement) to reach out and work with Sunnis and Kurds instead of marginalizing them.

In The New York Times, Alissa J. Rubin and Rod Nordland reported this week that Sunni Arab and Kurdish leaders met with al-Maliki, with the Sunnis proposing in effect a Sunni army to vanquish the militants. That would have been a perfect way to nurture unity and deploy moderate Sunnis to crush the militant Sunnis, defusing sectarian tensions. Instead, al-Maliki rejected the idea.

Many Sunnis in Iraq dislike the militants, but they have learned to loathe and distrust al-Maliki even more. The way out of the mess in Iraq is for the government to share power with Sunnis and Kurds, accept decentralization and empower moderate Sunni tribes.

If all that happens, it may be reasonable for the United States to back a united Iraqi government by authorizing air strikes against militant fighters. Without that, we simply become an accomplice to al-Maliki’s intransigence, assisting one party in a civil war. As Gen. David Petraeus told a London conference, “This cannot be the United States being the air force for Shia militias.”

Unfortunately, it looks as if al-Maliki is doubling down, revving up his Shiite base rather than building a common front. The Iraqi government should be releasing Sunni prisoners as a goodwill gesture. Instead, prisoners have been executed by police.

Military force can be a powerful, indispensable tool, as we saw in Kosovo and with the no-fly zone over Kurdistan. But the $4 trillion lesson from the Iraq War is that while our military capabilities are dazzling and sometimes intoxicating, they cannot be the solution to every problem.